TWO-PHASE FLOW IN A POROUS MEDIA TEST-CASES PERFORMED WITH TOUGH2
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1 TWO-PHASE FLOW IN A POROUS MEDIA TEST-CASES PERFORMED WITH TOUGH2 Paris 23 rd September 2010 E. Treille, J. Wendling Andra C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
2 Tough2 Overview (1/2) Code for multi-phase and multi-component fluid flow and transport in porous media Developed at Lawrence Berkeley National Laboratory (LBNL) Thermophysical fluid properties for a wide range of pressures and temperatures Many capillary pressure and relative permeability relationships Available version with FORTRAN 77 files of source code =>adaptable for specific needs: additional relationships (Problem4) additional outputs Specific fluid property modules: EOS5 for water/hydrogen mixtures (Problems 1-2-3) EOS3 for water/air mixtures (Problem 4) 2 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
3 Tough2 Overview (2/2) Space discretization is made from the integral form of the basic conservation equations (IFDM: integral finite difference method) Time is discretized fully implicitly (first-order) Linear equation system is solved using a Newton-Raphson iteration process Automatic time step control Primary variables (isothermal conditions): single phase conditions: P, X mass H2/air two-phase conditions: P g, S g primary variables are switched and re-initialized in response to a change of phase 3 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
4 Tough2 modules EOS3/EOS5 Components: water and hydrogen (EOS5) or air (EOS3) Phases: liquid and gas Ideal gas law for gas phase Dalton s law for partial pressures: P gas =P H2/air +P vap Fluid advection described with a multiphase extension of Darcy s law Solubility of hydrogen according to Henry s law: X mole =H*P H2/air 4 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
5 Main deviations from the test-cases specifications Diffusion model: i j α diffusive flux of component i in fluid phase j i α = φs ρ d X α α i α i α i with X α mass fraction of component i in phase α α Vapor pressure is not neglected: At 300 K saturated vapor pressure is 3532 Pa At 303 K saturated vapor pressure is 4205 Pa Compressibility of liquid water Production term for hydrogen: applied on a thin specific volume instead of a boundary surface 5 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
6 Problem 1: gas phase appearance/disappearance Porous media initially fully saturated with pure water Regular spatial discretization: dx=1 m Time discretization: dtmin=1 s, dtmax = 1000 years Relative convergence criterion: C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
7 Problem 1: gas phase appearance/disappearance Porous media initially fully saturated with pure water 7 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
8 Problem 1: gas phase appearance/disappearance Porous media initially fully saturated with pure water 8 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
9 Problem 1: gas phase appearance/disappearance Porous media initially partially saturated with liquid Regular spatial discretization: dx=1 m Time discretization: dtmin=1 s, dtmax = 1000 years Relative convergence criterion: C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
10 Problem 1: gas phase appearance/disappearance Porous media initially partially saturated with liquid 10 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
11 Problem 1: gas phase appearance/disappearance Porous media initially partially saturated with liquid 11 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
12 Problem 2: two-phase flow in a non homogeneous porous media Porous media initially partially saturated with liquid 12 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
13 Problem 2: two-phase flow in a non homogeneous porous media Porous media initially partially saturated with liquid 13 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
14 Problem 2: two-phase flow in a non homogeneous porous media Porous media initially fully saturated with pure water Regular spatial discretization: dx=1 m Time discretization: dtmin=1 s, dtmax = 1000 years Relative convergence criterion: C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
15 Problem 2: two-phase flow in a non homogeneous porous media Porous media initially fully saturated with pure water 15 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
16 Problem 2: two-phase flow in a non homogeneous porous media Porous media initially fully saturated with pure water 16 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
17 Problem 3: two-phase flow with non equilibrium states at initial time Regular spatial discretization: dx=0.005 m Time discretization: dtmin=1 s, dtmax = 1000 years Relative convergence criterion: C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
18 Problem 3: two-phase flow with non equilibrium states at initial time Two adjacent partially saturated zones at initial time 18 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
19 Problem 3: two-phase flow with non equilibrium states at initial time Two adjacent partially saturated zones at initial time 19 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
20 Problem 3: two-phase flow with non equilibrium states at initial time Two adjacent partially saturated zones at initial time 20 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
21 Problem 3: two-phase flow with non equilibrium states at initial time Left zone is fully liquid saturated at initial time 21 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
22 Problem 3: two-phase flow with non equilibrium states at initial time Left zone is fully liquid saturated at initial time 22 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
23 Problem 3: two-phase flow with non equilibrium states at initial time Left zone is fully liquid saturated at initial time 23 C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
24 Problem 4: two-phase flow with non equilibrium states at initial time Irregular spatial discretization: dxmax=2.25 cm, dxmin=0.02 cm Time discretization: dtmin=10 s, dtmax = 100 s Relative convergence criterion: C.TR.AEAP.1000xx AGENCE NATIONALE POUR LA GESTION DES DÉCHETS RADIOACTIFS
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